Kinematics

Question 1

What is the equation for velocity?

Answer 1

velocity = displacement / time

v = x / t

Question 2

What is the equation for speed?

Answer 2

speed = distance / time

s = d / t

Question 3

What is the equation for acceleration?

Answer 3

acceleration = change in velocity / time

a = §v / t

Question 4

How do we calculate instantaneous velocity?

Answer 4

Draw a tangent on a displacement / time graph and calculate.

Question 5

What is meant by the term acceleration?

Answer 5

If the velocity of a body is changing, it is said to be accelerating.

Question 6

How do we find the acceleration on a velocity-time graph?

Answer 6

To find the acceleration, we calculate the gradient of the line.

Question 7

How do we find the displacement on a velocity-time graph?

Answer 7

To find displacement, we work out the area underneath the line.

Question 8

Where does the equation v = u + at derive from?

Answer 8

{v = u + at} is a rearranged version of the equation {a = v - u / t} which is used to calculate acceleration.

Question 9

Where does the equation x=1/2(u+v)t derive from?

Answer 9

{x=1/2(u+v)t} comes from the formula of a trapezium, {A=1/2(a+b)h}.

Question 10

Where does the equation x=ut+1/2at^2 derive from?

Answer 10

{x=ut+1/2at^2} also comes from the area under a graph. However this time, the trapezium is split up into a rectangle and a triangle. So ut is from base × height, and 1/2at^2 is from 1/2bh but you then use {v=u+at} so you get {x=ut+1/2(u+at-u)t} where the u cancels out and the t becomes squared.

Question 11

Where does the equation {v^2=u^2+2ax} derive from?

Answer 11

{v^2=u^2+2ax} comes from {t=v-u/a} (the first SUVAT equation rearranged) and {x=1/2(u+v)t} (the second SUVAT equation. We get {2ax=(v+u)(v-u)} so {2ax= v^2-u^2} which we can rearrange to get {v^2=u^2+2ax}.

Question 12

What is a projectile?

Answer 12

A projectile is when an object is made to move obliquely upwards and carries on its horizontal path under gravity.

Question 13

If a ball is dropped vertically downwards and another ball is thrown horizontally, they will both hit the ground at the same time, why is this?

Answer 13

They will hit the ground at the same time as their horizontal and vertical motions are independent and don’t affect one another. They will both be accelerating downwards at 9.81ms^-1.

Question 14

What 2 mathematical formulas do we sometimes need to combine for projectiles?

Answer 14

For projectiles, we might need to do trigonometry to resolve a vector then SUVAT to calculate time or displacement.

Question 15

How can we measure gravity by free fall?

Answer 15

All we need to do to measure gravity by free fall is to measure a time (t) it takes for an object to fall from a known height (h).

Question 16

How can we find an equation for gravity from a free fall experiment?

Answer 16

We can use the equation {x=ut+1/2at^2} which has u=0 and a=g so we get {x=1/2gt^2} or we can rearrange and make g the subject: {g=2h/t^2}

Question 17

What is the gradient on a h-t^2 graph?

Answer 17

1/2g

Question 18

What is a problem with the measuring g from free fall experiment?

Answer 18

There may be a time delay between the time the stopwatch has been started and the time at which the ball is released from the electromagnet.

Question 19

How would you find the percentage uncertainty if the is 0.1s at 2s?

Answer 19

P = (0.1/2)×100 = 5%